1. Field of the Invention
The present invention relates to an electron microscope and, more particularly, to a technique that achieves performance comparable to that of a differential interference contrast method in visible light microscopy by forming interfering phases of electrons using a phase plate. This technique permits contrast improvement of electron microscope images and three-dimensional topographical imaging that is a novel method of representation. The invention also relates to a method using this technique.
2. Description of Related Art
Generally, there are four kinds of transmission microscopy that are fundamentally different in imaging method, i.e., a) bright field microscopy, b) dark field microscopy, c) phase contrast microscopy, and d) differential interference contrast microscopy.
Only bright field microscopy, dark field microscopy, and phase contrast microscopy have been realized in transmission electron microscopy for the following reason. In visible light microscopy, complex operations (i.e., splitting into two incident waves and recombination of the waves transmitted through a specimen) have been performed on incident waves in a real space. It is considered that it is technically difficult for the existing electron optical lens system to perform these complex operations. It is known that Schlieren technology is close to differential interference contrast microscopy and consists of inserting a field of view-cutting semicircular aperture into the focal plane behind the objective lens. This technology is also known as single-sideband holography (L. Reimer, Transmission Electron Microscopy: Physics of Image Formation and Microanalysis, Ed. 4, Springer, N.Y., 1997). However, this has not been used because half of the spatial-frequency components are discarded and because the resulting image is complex to interpret.
Differential interference contrast microscopy is used in visible light microscopy to topographically image variations in the phases of incident waves caused by a transparent specimen. The difference between the phase contrast microscopy used for a transparent specimen and differential interference contrast microscopy is that images not phases but their derivatives (which ought to be referred to as differences because they are differences in finite displacements) are used. Therefore, two Wollaston prisms are placed on the opposite sides of a specimen. The incident waves are split by the first prism into two beams slightly laterally displaced. After transmission through the specimen, the second prism recombines the two transmitted beams into one on the same optical axis, and the resulting interference is detected. Consequently, the lateral difference of the phase variation (phase difference) due to the specimen is converted into an intensity image. Thus, imaging is achieved.
Where the specimen is thin, the electron beam is little absorbed and almost fully transmitted. That is, it can be considered that what are treated by an electron microscope are transparent specimens. For this reason, the imaging method intrinsic to electron microscopy should be phase contrast microscopy or differential interference contrast microscopy, but neither of them are used today. With respect to the former technology, the principle is understood but the phase plate suffers from the problem of charging effects. On the other hand, where the latter technology is employed, if it is attempted to do work similar to the work done by the aforementioned real-space microscopy technique, it is necessary to combine biprisms and deflectors in a complex manner. Hence, it has been difficult to achieve a simple setup for electron microscopy unlike visible light optics.
Various operations in a real space can be often replaced by operations in a k-space, i.e., operations on the phases of electron waves at the back focal plane (diffraction plane) of an objective lens, if contrivances are made. One example is installation of a Zernike phase plate at the back focal plane (Japanese Patent Application No. 2000-85493 filed by Nagayama and Danev). Of course, in order that such operations are performed smoothly, the back focal plane is restricted to a point light source illumination system capable of clearly defining a back focal plane. As long as these conditions are met, achievements similar to those achieved by the differential interference contrast microscopy can be accomplished by installing a novel phase plate (i.e., a semicircular phase plate that blocks half of the field of view at the focal plane). This phase plate delays the phases of incident waves by xcfx80. Preferably, the phase plate is made of a thin amorphous film using a light element that shows a small degree of scattering. Examples include a film of amorphous carbon, a film of amorphous aluminum, and a film of amorphous silicon.
This is described in further detail by referring to the accompanying drawings. First, the phase plate is placed at the back focal plane (Pb) of an objective lens placed in a transmission electron microscope as shown in FIG. 11. Where incident electrons emerging from a point source do not provide strictly parallel illumination immediately ahead of the objective lens, the focus of the incident waves (the circle of least confusion) is shifted above or below the focal plane. In this case, a moving mechanism is necessary to move the phase plate holder into the focal point. The following description is given on the assumption that this moving mechanism is present.
FIG. 1 shows a semicircular phase plate according to the present invention. Normally, the phase plate inserted into the back focal plane (Pb) of the objective lens shown in FIG. 11 assumes a contour as shown in FIG. 1. The semicircular phase plate, indicated by numeral 1, consists of a thin film placed on a circular phase plate support 2. The semicircular plate 1 and the phase plate support 2 are collectively referred to as the phase plate assembly. It is assumed that the thin film of the phase plate 1 overlies the phase plate support 2.
FIG. 2a shows a plan view and FIG. 2b a side elevation of the phase plate assembly. FIG. 2a of the phase plate assembly is taken from above. The semicircle occupied by the phase plate assembly is referred to as the phase plate semicircle. The remaining semicircle is referred to as the semicircular opening. Transmitted, incident waves are brought to a focus at a point 3 through which the optical axis passes. This point is the zeroth-order diffraction point, and an adjustment is always made to place this point on the side of the semicircular opening. A side elevation of the phase plate assembly is shown in FIG. 2b. The relative arrangement of the two components of the phase plate assembly can be seen from FIGS. 2a and 2b. 
FIG. 3 shows the system of coordinates of the diffraction plane (focal plane) depending on the semicircular phase plate. A system of coordinates as shown in FIG. 3 is established around the phase plate assembly for correspondence with expansion of the theory. The focal point (zeroth-order diffraction point) of transmitted, incident waves is taken at the origin. Coordinate axes (kx, ky) corresponding to a Fourier-transformed k-space are placed on the focal plane as shown. The semicircular phase plate covers the half plane on the side kx  less than 0 as shown in FIG. 3. Note that kx and ky are x- and y-components, respectively, of two-dimensional spatial frequency vector xcexa. The vector xcexa is correlated with a real vector r on the focal plane by the following relational equation.                     κ        =                  r                      λ            ⁢                          xe2x80x83                        ⁢            f                                              (        1        )            
where xcex is the wavelength of electron waves and ƒ is the focal distance of the objective lens.
If electron waves pass through a thin film having a uniform thickness and uniform composition, the phases of the waves are shifted according to the following formula (D. Willasch, Optic 44 (1975) 17):                     φ        =                  -                                    π              ⁢                              (                                  h                  /                  λ                                )                            ⁢                              (                                  V                  /                                      U                    0                                                  )                            ⁢                              (                                  1                  +                                      2                    ⁢                    α                    ⁢                                          xe2x80x83                                        ⁢                                          U                      0                                                                      )                                                    (                              1                +                                  α                  ⁢                                      xe2x80x83                                    ⁢                                      U                    0                                                              )                                                          (        2        )            
where h is the thickness of the thin film of the phase plate, V is the internal potential of the thin-film material, U0 is the accelerating voltage, and xcex1 is a constant (=0.9785xc3x9710xe2x88x926Vxe2x88x921).
In FIG. 3, when the optical axis is brought infinitely close to the edge of the thin film, the action of the phase plate is represented by                     {                                                                              exp                  ⁡                                      (                                          ⅈ                      ⁢                                              xe2x80x83                                            ⁢                      φ                                        )                                                  ,                                                                                      k                  x                                 less than                 0                                                                                        1                ,                                                                                      k                  x                                ≥                0                                                    }                            (        3        )            
where exp (ixcfx86) is applied to half plane of the k-space image of scattering waves. If a weak object that causes small variations in amplitude and phase is used as the specimen, almost every entering wave passes through the focal point 3 without being scattered. The effects of the phase plate assembly appear as modulation of the amplitude and phase due to the following contrast transfer functions (CTFs):
amplitude CTF: 2 cos [xcex3(|xcexa|)+xcfx86/2]exp(xe2x88x92i sgn(kx)xcfx86/2)xe2x80x83xe2x80x83(4) 
phase CTF:xe2x88x922 sin [xcex3(|xcexa|)+xcfx86/2]exp(xe2x88x92i sgn(kx)xcfx86/2)xe2x80x83xe2x80x83(5) 
where sgn (kx) is a signum function, and we have sgn (kx)=1 (kxxe2x89xa70) and sgn (kx)=xe2x88x921 (kx less than 0). xcex3(|xcexa|) is a phase delay caused by the spherical aberration of the objective lens and by defocus. The phase delay is dependent on the spatial frequency and given by the following formula (L. Reimer):                               γ          ⁡                      (                          "LeftBracketingBar"              κ              "RightBracketingBar"                        )                          =                  2          ⁢                      π            ⁡                          (                                                -                                                            λ                      ⁢                                              xe2x80x83                                            ⁢                      Δ                      ⁢                                              xe2x80x83                                            ⁢                      Z                      ⁢                                              xe2x80x83                                            ⁢                                              k                        2                                                              2                                                  +                                                                            λ                      3                                        ⁢                    Cs                    ⁢                                          xe2x80x83                                        ⁢                                          k                      4                                                        4                                            )                                                          (        6        )            
where Cs is the spherical aberration coefficient and xcex94Z is the defocus.
Where the phase plate is removed (xcfx86=0 in Eq. (3)), the above-described Eqs. (4) and (5) are, respectively, given by
amplitude CTF: 2 cos xcex3(|xcexa|)xe2x80x83xe2x80x83(7) 
phase CTF:xe2x88x922 sin xcex3(|xcexa|)xe2x80x83xe2x80x83(8) 
It follows that CTFs appearing in normal electron microscopy are obtained.
Especially, in the case of an extremely thin specimen, little amplitude variation occurs and so the phase CTF is applied to the phase component and converted into an intensity image, which is observed. In normal electron microscopy, this sine-type CTF has presented various problems including low contrast and modulation of the image.
With respect to xcfx86, the case where xcfx86=xe2x88x92xcfx80 is especially important in specific applications. By inserting xcfx86=xe2x88x92xcfx80 into Eqs. (4) and (5) gives rise to exp (i sgn (kx)xcfx80/2) =i sgn (kx). Therefore, Eqs. (4) and (5) are, respectively, simplified into the forms:
amplitude CTF: i 2 sgn(kx)sin xcex3(|xcexa|)xe2x80x83xe2x80x83(9) 
phase CTF: i2sgn(kx)cos xcex3(|xcexa|)xe2x80x83xe2x80x83(10) 
This is illustrated in FIGS. 4a and 4b, which depict the results of simulations of the contrast transfer functions (CTFs) of a differential contrast microscope where the phase delay of the semicircular phase plate is xcfx80, the defocus is 0, and the accelerating voltage is 300 kV. FIG. 4a indicates the CTF applied to the amplitude, while FIG. 4b indicates the phase CTF applied to phase components.
Compared with the CTFs (Eqs. (7) and (8)) of normal electron microscopy, three distinct features are observed. The first one is that the corresponding relations with the sine function and cosine function are exchanged and cos xcex3(|xcexa|) appears in the phase CTF. The second one is that the signum function sgn (kx) is applied. As a result, the amplitude and phase CTFs which are intrinsically even functions are converted into odd functions. The third one is that the imaginary unit i is applied. The first feature means that the image contrast in the phase object is improved, because the phase CTF is the same contrast transfer function as a phase contrast image. The third feature is not intrinsic. It is a factor for obtaining a real function in a Fourier-transformed real space. An important feature appears as the second feature. CTFs which were even functions are changed into odd functions. This can lead to a differential contrast image. This is hereinafter described in detail.
Eq. (10) is approximated by the sum of two rectangular functions: (xe2x88x92Π(kx/kc +xc2xd)+Π(kx/kcxe2x88x92xc2xd)). FIGS. 5a and 5b represent the differential contrast where this approximate phase CTF is used. The phase CTF of FIG. 4b is approximated by two rectangular functions (Π(x)) having opposite signs. The frequency of the first zero point in FIG. 4b is made to correspond to kc. Because signals appearing in the range given by |xcexa| greater than kc are averaged out to zero in the original function by fast vibrational modulation occurring in this range, |xcexa| greater than kc is set to 0.
FIG. 5b is the Fourier transform of the rectangular function (FIG. 5a) of the opposite sign used for the approximation and given by                               ⅈ          ⁢                      xe2x80x83                    ⁢                                    (                              sin                ⁢                                  xe2x80x83                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                                  k                  c                                ⁢                x                            )                        2                                    π          ⁢                      xe2x80x83                    ⁢                      k            c                    ⁢          x                                    (        11        )            
The Fourier transform of a CTF acting on phase components gives a point spread function of a real-space image. Therefore, FIG. 5b indicates a point spread function, i.e., the degree of blurring of an image when an infinitesimally small point forms an image. The action is equivalent to the case where the function of Eq. (11) is convolved to an ideal image of positive focus (which may be referred to as the original image) without aberration.
Eq. (11) can be rewritten into the form sin xcfx80kc xxc2x7sinc (xcfx80kcx). The action of the first term sin xcfx80kcx is to shift the sinc function (sinc (xcfx80kcx)=sin xcfx80 kc x/xcfx80 kc x) to the right and left, thus changing the sign. The result is the sum of two functions of opposite signs as can be seen from FIG. 5b. Eq. (11) can be represented in terms of the sum of xcex4 functions which have opposite signs and are spaced apart by 1/kc. Thus,                               δ          ⁡                      (                          x              +                              1                                  k                  c                                                      )                          -                  δ          ⁡                      (                          x              -                              1                                  k                  c                                                      )                                              (        12        )            
An actual image is the superimposition of its approximate formula (Eq. (12)) and the original image. It follows that their difference is created.
Specifically, this process is equivalent to shifting the original image to the left and right by xc2xdkc and taking the difference between them because they are opposite in sign. The displacement xc2xdkc will be determined from the position of the first zero point in the CTF of FIG. 4b. In practice, since it is the superimposition of sinc functions, the original image has a point spread determined by the functions and thus the resolution is limited.
The principle of a differential contrast microscope has been described thus far. The differential nature and the property that a phase CTF changes into cos xcex3(|xcexa|) (i.e., characteristic equivalent to the differential phase microscopy) are all derived from the fact that CTFs are converted into odd functions. The conversion to odd functions arises from the following formula that is a function form of a phase plate:                               sgn          ⁡                      (                          k              x                        )                          =                  {                                                                                          -                    1                                    ,                                                                                                  k                    x                                     less than                   0                                                                                                      1                  ,                                                                                                  k                    x                                     greater than                   0                                                              }                                    (        13        )            
The property of this differential contrast microscopy is common with the differential interference contrast microscopy utilized in visible light microscopy in terms of the following two points: 1) the technology is differential microscopy, and 2) the CTF is the same as that of a phase difference image. Because of these features, the resulting image is a three-dimensional topographical representation as shown in FIGS. 8a-8f. Therefore, this technology may be referred to as differential interference contrast microscopy. However, the present invention adopts a totally new method consisting of performing operations on phases in a k-space. To avoid confusion, a new term xe2x80x9cdifferential contrast microscopyxe2x80x9d is introduced.
An operation for numerically returning the signum modulation of kx-plane that is a characteristic of differential microscopy to the original state is now discussed. This is achieved by performing a multiplication operation of the following function on the Fourier-transformed image of the obtained image:                               1          2                ⁢        exp        ⁢                  xe2x80x83                ⁢                  (                      ⅈ            ⁢                          xe2x80x83                        ⁢                          sgn              ⁡                              (                                  k                  x                                )                                              )                ⁢                  φ          2                                    (        14        )            
This function form is multiplied with the intrinsic CTFs (4) and (5), resulting in the following CTFs:                               amplitude            CTF          :                ⁢                  xe2x80x83                ⁢                  cos          ⁡                      (                                          γ                ⁡                                  (                                      "LeftBracketingBar"                    κ                    "RightBracketingBar"                                    )                                            +                              φ                2                                      )                                              (        15        )                                          phase            CTF          :                ⁢                  xe2x80x83                -                  sin          ⁡                      (                                          γ                ⁡                                  (                                      "LeftBracketingBar"                    κ                    "RightBracketingBar"                                    )                                            +                              φ                2                                      )                                              (        16        )            
These CTFs are even functions unlike the CTFs of FIGS. 4a and 4b and do not exhibit conspicuous differential effects. Where xcfx86=xe2x88x92xcfx80 is substituted into Eqs. (15) and (16), the CTFs are changed into the following even functions:
amplitude CTF: sin xcex3(|xcexa|)xe2x80x83xe2x80x83(17) 
phase CTF: cos xcex3(|xcexa|)xe2x80x83xe2x80x83(18) 
These CTFs are nothing other than CTFs appearing in phase contrast microscopy using a Zernike phase plate (the above-cited Japanese Patent Application No. 2000-85493 filed by Nagayama and Danev; R. Danev and K. Nakayama, Ultramicroscopy 88 (2001) 243).
After this manner, a phase difference contrast image is reproduced by Fourier-transforming a differential contrast image and performing a multiplication processing of the function of Eq. (14) on the Fourier-transformed image.
Furthermore, the inventors of this application proposed a complex observational method (K. Nagayama, J. Phys. Soc. of Jpn. 68 (1999) 811; R. Danev and K. Nagayama, J. Phys. Soc. of Jpn. 70 (2001) 696). In the complex observational method, a complex image is obtained by combination between a phase difference contrast image and a normal electron microscope image concerning the same specimen. The phase difference contrast image is obtained in phase contrast microscopy.
According to the complex observational method, if the phase difference contrast image reproduced from the above-mentioned differential contrast image is combined with the normal electron microscope image concerning the same specimen, the complex image is obtained.
Other objects and features of the invention will appear in the course of the description thereof, which follows.